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Chapter 5: Problem 45
Verify each identity. $$\cos (\alpha+\beta) \cos (\alpha-\beta)=\cos ^{2} \beta-\sin ^{2} \alpha$$
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Use the power-reducing formulas to rewrite \(\sin ^{6} x\) as an equivalent expression that does not contain powers of trigonometric functions greater than 1
Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$\cos x \csc x=2 \cos x$$
Remembering the six sum and difference identities can be difficult. Did you have problems with some exercises because the identity you were using in your head turned out to be an incorrect formula? Are there easy ways to remember the six new identities presented in this section? Group members should address this question, considering one identity at a time. For each formula, list ways to make it casier to remember.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. In order to simplify \(\frac{\cos x}{1-\sin x}-\frac{\sin x}{\cos x},\) I need to know how to subtract rational expressions with unlike denominators.
Graph each side of the equation in the same viewing rectangle. If the graphs appear to coincide, verify that the equation is an identity. If the graphs do not appear to coincide, this indicates the equation is not an identity. In these exercises, find a value of \(x\) for which both sides are defined but not equal. $$\sin x-\sin x \cos ^{2} x=\sin ^{3} x$$
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